This is not a correct interpretation. Instead, Paul says in Romans 13 that the idea of government is God's idea to establish and maintain order in society, but he didn't claim that earthly authority always did God's will. The Gospels are clear that Jesus did not accept all legal and governing authorities as ultimate dispensers of God’s will. Most of the references to the “Powers” in the NT consider them as fallen. Yet despite their fallen condition, the Powers cannot fully escape the providential sovereignty of God. He is still able to use them for good, and sometimes does.

Paul’s view of earthly authority is that it always does God’s will (Romans 13).

It refers to earthly rulers, contrary to what you are saying. Check out 1 Cor. 1.26-28 for context. Paul is saying we don't follow the wisdom of earthly rulers; the wisdom of this world will amount to only a hill of beans. When Paul says they are "coming to nothing," he uses the present participle to note that they are in that process—in that direction. The purposes of God in choosing the “foolish,” the “weak,” the “low and despised,” and “things that are not” (cf. 1.27-28) was already starting to happen.

Then he says (1 Cor. 2.8) that none of these political and religious leaders (notably Caiaphas, Annas, Herod and Pilate) understood the mystery of God in Christ (v. 7). if they had, they would have bowed in worship rather than crucified Him in shame.

In 1 Cor. 2:6-9 Paul says that the ‘the rulers of this age’ are being destroyed.

This can't refer to Rome and Jewish authorities who were at the height of their power.

Paul says that if these rulers had known that eternal life would be the effect of his death, they would not have killed him.

Thus rulers can't refer to humans.

Humans would want eternal life.

However the word ruler also refers to demons.

For example Ephesians 2.2.